Are textureless scenes recoverable?

It is widely accepted that textureless surfaces cannot be recovered using passive sensing techniques. The problem is approached by viewing image formation as a fully three-dimensional mapping. It is shown that the lens encodes structural information of the scene within a compact three-dimensional space behind it. After analyzing the information content of this space and by using its properties we derive necessary and sufficient conditions for the recovery of textureless scenes. Based on these conditions, a simple procedure for recovering textureless scenes is described. We experimentally demonstrate the recovery of three textureless surfaces, namely, a line, a plane, and a paraboloid. Since textureless surfaces represent the worst case recovery scenario, all the results and the recovery procedure are naturally applicable to scenes with texture